Individual-based population with energy budgets

Field: ecology · Zoo name: energy_budget · Module: modelly.zoo.energy_budget.model

Foragers walk a grid on which a resource flows in at a constant rate per cell. Every step each forager moves to a random neighbouring cell, the foragers in a cell share its resource equally and turn it into energy with an assimilation efficiency, and each pays a metabolic cost. A forager whose energy reaches birth_threshold splits it with an offspring in its cell; one whose energy falls below zero starves. Nothing but energy regulates the population.

How it is written

Foragers keep their energy and the row of their cell in Column arrays and are placed by row (CellIndex.track), so no cell keeps a list of agents. Moving is CellIndex.random_neighbor, sharing is CellIndex.counts, starving is ColumnTable.remove_where; only births create objects (ColumnTable.do_where).

from modelly.zoo.energy_budget.model import EnergyBudget, EnergyScenario

model = EnergyBudget(EnergyScenario(rng=42))
model.run()
model.population(), model.carrying_capacity()
model.datacollector.get_model_vars_dataframe()  # foragers and uneaten resource per step

Parameter	Default	Meaning
width, height	30, 30	grid size in cells
initial	100	foragers at the start
initial_energy	5.0	energy of each initial forager
inflow	1.0	resource added to every cell per step
efficiency	0.5	share of the eaten resource turned into energy
cost	1.0	energy spent per forager per step
birth_threshold	10.0	energy at which a forager splits with an offspring
steps	400	run length of run()

Validation

The resource is never capped and is eaten whenever a forager visits, so in the long run all of it is eaten. At equilibrium the energy assimilated equals the energy spent, efficiency * inflow * cells = cost * N, which gives the carrying capacity K = efficiency * inflow * cells / cost (450 with the defaults). The only other energy leaving the balance is the deficit of starving foragers, at most one cost each, which keeps the mean population at or slightly above K.

tests/zoo/test_energy_budget.py checks, for three seeds and two inflows, that the mean population after a burn-in of 150 steps is within 3 % of K (the step-to-step fluctuation is about 2 % of K, and averaging 250 steps leaves well under 1 %); that the uneaten stock stays bounded; that the population dies out without inflow; and that the same seed gives the same population curve.

References

• Grimm, V. and Railsback, S. F. (2005). Individual-based Modeling and Ecology. Princeton University Press.

Start a project from it with modelly zoo copy energy_budget my_population.